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Theorem imp5d 357
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp5d (((𝜑𝜓) ∧ 𝜒) → ((𝜃𝜏) → 𝜂))

Proof of Theorem imp5d
StepHypRef Expression
1 imp5.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21imp31 254 . 2 (((𝜑𝜓) ∧ 𝜒) → (𝜃 → (𝜏𝜂)))
32impd 252 1 (((𝜑𝜓) ∧ 𝜒) → ((𝜃𝜏) → 𝜂))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106
This theorem is referenced by: (None)
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